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On paraquaternionic submersions between paraquaternionic Kähler manifolds. (English) Zbl 1200.53027

Summary: In this paper we deal with some properties of a class of semi-Riemannian submersions between manifolds endowed with paraquaternionic structures, proving a result of non-existence of paraquaternionic submersions between paraquaternionic Kähler non-locally hyper para-Kähler manifolds. Then we examine, as an example, the canonical projection of the tangent bundle, endowed with the Sasaki metric, of an almost paraquaternionic Hermitian manifold.

MSC:

53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
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